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Fatigue Life Prediction of Shot Peening R. A. Cláudio et al.
Ciência e Tecnologia dos Materiais, Vol. 20, n.º 1/2, 2008 99
Fatigue Life Prediction of Shot Peening R. A. Cláudio et al.
Ciência e Tecnologia dos Materiais, Vol. 20, n.º 1/2, 2008 99
FATIGUE LIFE PREDICTION OF SHOT PEENED COMPONENTS
R.A. CLÁUDIO*1
, J.M. SILVA2, C.M. BRANCO
3, J. BYRNE
4
1Department of Mechanical Engineering, ESTSetúbal/Instituto Politécnico de Setúbal
Campus do IPS, Estefanilha, 2910-761 Setúbal.2Department of Aerospace Sciences, Universidade da Beira Interior,
Edifício II das Engenharias, 6201-001, Covilhã. 3Department of Mechanical Engineering, Instituto Superior Técnico
Av. Rovisco Pais, 1049-001 Lisboa.4Department of Mechanical and Design Engineering,
University of Portsmouth, Portsmouth, Hants PO1 3DJ, UK
ABSTRACT: Shot peening is one of the most effective surface treatments in order to prevent crack initiation and early
crack propagation. Part of the studies to determine the fatigue performance of shot peening are based on experimental
tests. Almost no work is published related with the prediction of shot peening behaviour. The present paper evaluates the
ability of the current methodologies, used to predict fatigue life, on components treated with shot peening. The Finite
Element Method was used to determine the stress, strain and strain energy due to shot peening of some specimens tested
experimentally. These results were used to apply methods to predict the total fatigue life. A final discussion is presented
about the ability of the methods used, to predict the fatigue life of the specimens tested experimentally.
Keywords: Shot Peening, Fatigue Life Prediction, Finite Element Method.
RESUMO: A grenalhagem é um dos tratamentos mais eficientes na prevenção da iniciação de fendas por fadiga e na fase
inicial de propagação. Grande parte dos estudos sobre o feito da grenalhagem no comportamento à fadiga são
experimentais. Praticamente não existem trabalhos publicados relativos ao estudo de previsão do comportamento da
grenalhagem. Neste trabalho são usados modelos tradicionais, de determinação da vida à fadiga, em componentes
grenalhados. O método dos elementos finitos é usado para determinar a tensão, extensão e energia de deformação de
provetes grenalhados que foram testados experimentalmente. Estes resultados são usados em m odelos de previsão da vida
total à fadiga. É apresentada uma discussão sobre a capacidade dos modelos usados na previsão de vida à fadiga de
provetes que foram testados experimentalmente.
Palavras chave: Grenalhagem, Previsão de Vida à Fadiga, Método dos Elementos Finitos.
1. INTRODUCTION
Shot peening is a cold work process that induces a
protective layer of compressive residual stress at the surface
of components. The objective of that compressive layer is to
offset the applied stress, resulting in a benefit in terms of
fatigue, corrosion-fatigue and fretting fatigue, [1]. In order
to produce plastic deformation, a stream of metal, glass or
silica particles (“shot”) is animated at high velocity and
projected against the surface of the metallic component in a
defined and controlled way.
In reference [2] is a study of the increase in fatigue life that
it is possible to achieve with an appropriate use of shot
peening. Some of these examples are: leafs spring - 600%
increase; helicoidal springs - 1300%; gears - 1500%. These
are some impressive examples how much life improvement
is possible with shot peening. The main importance of shot
peening is because it acts at the surface of components
reducing the effective stress due to the compressive layer.
This layer is only of some hundreds of microns depth, but
enough to be quite effective. Some improvement is also
attributed to the strain hardening due to plastic work at
surface. However it is also necessary to account for the
increase of surface roughness which has a negative
contribute to the fatigue improvement. Normally it is
assumed that the contribute due to strain hardening is
balanced by the increase in surface roughness.
Numerical modelling of fatigue behaviour of shot peened
components is a main subject of a considerable number of
papers oriented to the numerical simulation of the related
residual stress fields [3-8]. Many other works can be found
trying to model the effect of shot peening parameters on the
residual stress profile, [9-15]. From all these works it is
possible to conclude that much more is necessary to
R. A. Cláudio et al. Fatigue Life Prediction of Shot Peening
100 Ciência e Tecnologia dos Materiais, Vol. 20, n.º 1/2, 2008
R. A. Cláudio et al. Fatigue Life Prediction of Shot Peening
100 Ciência e Tecnologia dos Materiais, Vol. 20, n.º 1/2, 2008
simulate the effect of shot peening. In many of these works,
the shot peening model is limited to only one shot.
Considering 3D simulations, the most complete model
include the effect of only 3 shots which only proves that
modelling of residual stress induced by shot peening is a
quite complex matter which requires further developments.
The number of publications related with fatigue life
prediction of shot peening is even scarcer. Sherrat [16],
points some of the principal reasons why shot peening is so
difficult to be fatigue predicted:
- Peening has influence on crack initiation as well on
propagation. Fracture mechanics will give no guidance on
this, and local strain calculations are little better;
- The surface left by peening will be complicated in its
texture;
- Fracture mechanics does not predict the behaviour of short
cracks, which is important in the shot peening calculation.
De Los Rios et al. [17], concluded that most of the analyses
made up till 1995, were based on simple superposition of the
residual stress in order to give the local surface stress, which
is a very simplistic approach, as in the cases of the work of
Li et al. [18] and John et al. [19].
A complete work about simulation of residual stress under
high cycle fatigue (HCF) was published by Fathallah [10].
His model is based on a multi-axial fatigue criteria and it
accounts for the residual stress profile, strain-hardening at
the surface and surface imperfections but does not account
for any cyclic relaxation. Apart from that, good
experimental agreement was found.
Giuseppe and Taylor [21], presented a recent work
modelling the effect of shot peening using the theory of
critical distances (point and line method). The residual stress
was treated as a mean stress using the Goodman approach,
however the contents of this work are limited to HCF
conditions.
In the present work, fatigue life will be predicted under low
cycle fatigue conditions (LCF). The finite element method
(FEM) will be used to determine the stress, strain and strain
energy to apply in total fatigue methods. Some
considerations about these methods can be found in [22].
2. FE MODEL
The geometry used as a reference for the FE analysis is a
washer specimen presented in Figure 1. The “washer”
specimen is used by Rolls Royce since it is representative of
a critical region of a gas turbine aero engine compressor
disc. The axis system represented will be used in the rest of
this work. This specimen was used because it was
previously fatigue tested, whose results can be found in [23].
A 2D non-linear FE model was built to determine the stress,
strain and strain energy in specimens with both as machined
and shot peened superficial conditions. These results will be
used in fatigue life models, in order to predict the fatigue
life, and to compare the numerical results with experimental.
The final objective of this work is to evaluate which is the
best method when considering the prediction of the shot
penning effect.
Fig. 1. Washer specimen and FE model.
Only half of the geometry was modelled because of
symmetry conditions. A quadrangular mesh was made with
biquadratic 2D plane strain elements (8 nodes), with two
degrees of freedom per node. Boundary conditions and
loading were set according to Figure 2. The applied load
was normalized to the critical section, not considering the
notch root, which has a cross sectional area (CSA) of
88.5508.511 =× mm2. In this region the specimen has a
curvature radius of 4.5mm with an elastic stress
concentration factor 32.1=tK . The values presented in the
labels of some figures are the maximum load of the loading
cycle. The loading cycle applied is trapezoidal with timings
1-1-1-1s and a loading ratio of R=0.1. These parameters are
identical to those used in experimental tests [23].
Fig. 2. Washer specimen 2D FE model for stress analysis.
In order to simulate residual stress due to shot peening a
thermal gradient was introduced with the same profile as the
residual stress in Figure 6. A direct relation between stress
and temperature was guaranteed by setting the thermal
expansion factor to 1/E, being E the young modulus of the
material at 650ºC. This method was successfully applied
before by Cook, Timbrell et al. [24]. More details can be
found in [22]. Part of the FE model is similar to the one
described in [25].
-1000
-800
-600
-400
-200
0
200
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Depth [mm]
Str
ess [
MP
a]
or
Tem
pera
ture
[ºC
]
Stress direction xx
Stress direction yy
Stress direction zz
Temperature Introduced (x-1)
Fig. 3. Residual stress profile calculated by FE due to the
introduction of a temperature profile.
Fatigue Life Prediction of Shot Peening R. A. Cláudio et al.
Ciência e Tecnologia dos Materiais, Vol. 20, n.º 1/2, 2008 101
Fatigue Life Prediction of Shot Peening R. A. Cláudio et al.
Ciência e Tecnologia dos Materiais, Vol. 20, n.º 1/2, 2008 101
3. MATERIAL PROPERTIES
The material considered in this investigation is a new
generation nickel base superalloy developed using a powder
metallurgy (PM) technique, whose commercial name is
RR1000. Chaboche model was used to define cyclic
material behaviour, whose parameters are listed below, [26].
Yield stress at zero plastic strain:
MPao
695=σKinematic hardening parameters,
61.391;10141 2 =×= γMPaC
Isotropic hardening parameters, 13.7;52.161 ==∞ bMPaQ
In order to calculate fatigue life for the simulated conditions
by FE, low cycle fatigue (LCF) data is needed. Zhan [27],
made fatigue tests for five specimens, using the same
frequency, same waveform and same temperature as the
ones used in this work. The Coffin-Mason parameter,
obtained from Zhan’s experimental data, are given by
equation (1):
( ) ( ) 048.0440.0
2
−×=Δff ((((ε
(1)
Equation (2) gives the S-N equation for RR1000 tested at
650ºC by Zhan, [27]. Experimental data to build this S-N
curve was taken from LCF tests, being the stress taken from
completely stabilized cycles.
( ) 1606.03.2708
−×= fa ((σ (2)
The total energy density, tWtΔ , was also used as a damaging
parameter. Total energy density, is the summation of the
elastic and plastic strain energy densities per cycle. To
account for mean stress the elastic strain energy density was
modified to account only for the tensile stress [28]. The total
strain energy density is given by equation (3).
( ) FLaffpet WFNA((fWpWeWt Δ+×==Δ+Δ=Δ +
(3)
where: +Δ eWe is the modified elastic strain energy density
pWpΔ is the plastic strain energy density
A and α are material constants
FLWFΔ is the strain energy density at the fatigue limit of
the material.
From Zhan’s experimental tests [27] and using the
Chaboche material parameters, a numerical simulation was
done in a plain specimen in order to obtain the total strain
energy density. This energy was calculated after cycle
stabilization. Equation (4) gives the relation between strain
energy and number of cycles to failure.
03.27.103302053.1 +×=Δ −
ft NWt (4)
4. STRESS, STRAIN AND STRAIN ENERGY IN THECRITICAL SECTION
The stress, strain and strain energy were calculated using the
FE solutions in order to apply fatigue life prediction
methods. These quantities are plotted in Figures 4 to 7, from
surface up to 0.5 mm depth (line between the notch root
(coordinates (0, 0, 0)) and the middle of the specimen
(coordinates (0, -2.54, 0)), Figure 2).
The results without shot peening are plotted in the graphs by
open symbols and dashed lines. Results that included shot
peening are with closed symbols and continuous lines. The
stress level (nominal stress over the critical section, as
described in section 2) was chosen so that failure should
occur between 103 and 105 cycles. This information was
taken from experimental tests. FE simulations were stopped
when the cyclic hysteresis loop was stable. For almost all
the loading situations, cyclic stabilization occurred after
some tens of cycles. Because of computational resources
and for some situations (mainly those with higher loading
levels) the simulation was stopped after 400 cycles, even if
the cyclic hysteresis loop was not totally completed.
The relaxation of residual stress, due to cyclic loading, was
already studied is in a previous work [25].
Figure 4 presents the stress range considered for the situations
studied. As it can be seen, shot peening does not affect thet
stress range, having effect only for mean stress levels, Figure
5. The effect of shot peening is perfectly clear up to 0.12 mm
depth. At the surface, initial residual stress almost vanishes
but it is still possible to notice a mean stress reduction of
about 40 MPa. Mean stress is higher for depths deeper than
0.12 mm when initial stresses are introduced, being this effect
related with the equilibrium of stress that must exist.f
0
500
1000
1500
0 0.1 0.2 0.3 0.4 0.5
��[[M[[PaPP
]aa
Depth [mm]
NoSP CSA 900MPa
SP CSA 900MPa
NoSP CSA 1000MPa
SP CSA 1000MPa
NoSP CSA 1100MPa
SP CSA 1100 MPa
Fig. 4. Stress range after hysteresis loop stabilization for the
washer specimen with and without shot peening (data points
for NoSP and SP are coincident).
Similar conclusions taken for stress can be observed when
analysing the strain curves. Figure 6 shows the strain range,
for the conditions studied. Strain range is exactly the same
for the conditions with and without initial residual stress, as
verified for the stress.
Figure 7 shows the strain energy density range, for the
conditions studied. The strain energy density plotted
includes the modification to account for mean stress effects,
[28]. For more information see [22].
Figure 7 allows inferring most of the conclusions formed
when stress range and mean stress were analysed. Without a
R. A. Cláudio et al. Fatigue Life Prediction of Shot Peening
102 Ciência e Tecnologia dos Materiais, Vol. 20, n.º 1/2, 2008
R. A. Cláudio et al. Fatigue Life Prediction of Shot Peening
102 Ciência e Tecnologia dos Materiais, Vol. 20, n.º 1/2, 2008
scratch it is possible to observe a large benefit of residual
stress up to 0.12 mm, whilst, for higher depths, strain energy
density evinces higher levels with the presence of residual
stress. At the surface the benefit is quite small.
-200
0
200
400
600
800
0 0.1 0.2 0.3 0.4 0.5.0
�mm[M[[PaPP
]aa
Depth [mm]
NoSP CSA 900MPa
SP CSA 900MPa
NoSP CSA1000 MPa
SP CSA 1000 MPa
NoSP CSA 1100MPa
SP CSA 1100MPa
Fig. 5. Mean stress after hysteresis loop stabilization for the
washer specimen with and without shot peening.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0 0.1 0.2 0.3 0.4 0.5
��5�55�55��55�5�5���5���
Depth [mm]
NoSP CSA 900MPa
SP CSA 900MPa
NoSP CSA1000 MPa
SP CSA 1000 MPa
NoSP CSA 1100MPa
SP CSA 1100MPa
Fig. 6. Strain range after hysteresis loop stabilization for the
washer specimen with and without shot peening.
0
0.5
1
1.5
2
2.5
3
3.5
4
0 0.1 0.2 0.3 0.4 0.5
�Wt[ttM[[J/JJm//
3]
33
Depth [mm]
NoSP CSA 900MPa
SP CSA 900MPa
NoSP CSA1000 MPa
SP CSA 1000 MPa
NoSP CSA 1100MPa
SP CSA 1100MPa
Fig. 7. Total strain energy range after hysteresis loop
stabilization for the washer specimen with and without shot
peening.
5. FATIGUE LIFE ASSESSMENT
Fatigue life was calculated from FE results, applying some total
fatigue methods normally used to access fatigue life, to verify
which one is the more appropriate to fit experimental results.
Table 1 presents the fatigue life predictions, for the stress
life method, using different criteria to consider the used
stress. The stress life method is more appropriate for HCF
conditions, where elastic stress profiles are frequently used.
For the application herein studied, the number of cycles to
failure indicates LCF conditions. In order to try to apply the
stress life method, to LCF conditions, the elastic-plastic
stress profile was used instead of the linear elastic one.
Simulations, not published, showed that life predictions with
linear elastic stress profiles gave unrealistic life results.
Fatigue life was obtained from the Basquin equation whose
parameters are in section 3. The Goodman criterion was
used to correct for mean stress effects.
In Table 1, the first column of fatigue results refers to the
“Hot spot method”, in which the stress used to calculate
fatigue life was taken exactly at the surface. The next five
columns refer to the line method. The quantity
a0 = 0.0171 mm is the El Haddad et al. constant [29], which
is determined using fatigue parameters for RR1000 at
650ºC.0
2a is the distance from the scratch tip to average
the stress profile according to the line method. As0
a is a
parameter calculated from linear elastic parameters
(assuming low plasticity), fatigue life was also determined
calculating the mean stress at a critical distance of 0.1 and
0.2 mm in order to check if results led to better predictions.
A weight function, ( )ϕ imilar to the one used by Lanning
et al.[30], was applied to give more relevance to the stress at
the scratch root when compared with the interior positions.
The weight function used is given by equation (5).
( )m
efx
x−= 1ϕ( (4)
where efx is the critical distance.
The exponent m used was m=1. For bigger values of m,
fatigue life prediction does not change significantly.
In the last column of Table 1, fatigue life predictions are
presents considering the SFI (Stress field intensity method)
model, which is based on the local elastic-plastic stress
profile. The major difficulty when applying this method is to
find the critical distance by observing the stress profile. For
higher loads or when residual stress is considered, the stress
profile does not behave as expected, since the definition of
the critical distance is not quite accurate. It should be noted
that the calculated fatigue life is strongly dependent on the
value obtained for the critical distance.
The results of Table 1, allow concluding that the greater is the
distance to average stress from the surface, the greater is the
life predicted. Stress levels near the surface are very high
resulting in lower life predictions. The use of a weight
function, ( )ϕ , to give more relevance to the stress values at
the surface does not significantly change the obtained results.
Fatigue life predictions made by the strain life method are in
Table 2. The strain-life curve was obtained from previous
LCF tests whose parameters are in section 3. The values of
strain range and mean stress were taken at the surface from
FE results. The expression proposed by SWT (Smith,
Watson and Topper method) [38] was used to account for
mean stress effects. The predicted life for the specimens
without shot peening is about ½ of the experimental results,
which is not a bad result taking in account fatigue results.
However the predicted life for the shot peening condition is
much lower than expected.
Fatigue Life Prediction of Shot Peening R. A. Cláudio et al.
Ciência e Tecnologia dos Materiais, Vol. 20, n.º 1/2, 2008 103
Fatigue Life Prediction of Shot Peening R. A. Cláudio et al.
Ciência e Tecnologia dos Materiais, Vol. 20, n.º 1/2, 2008 103
Table 1 – Fatigue life predictions by the stress life approach.
Life Predicted [Cycles]
Critical distance line method SP
CSAStress [MPa]
Experimental[Cycles] Hot spot
stress 0
2a 0.1mm0.1mm+ ( )( )ϕ 0.2mm 0.2mm +
( )( )ϕSFI
NO 59193 17407 18009 194 800 99 18831 21762 20346 22738
NO 29393 11739 12132 131 850 02 12667 14577 13654 16197
NO 15191 8058 8317 8958900 8671 9932 9323 11425
NO 8137 5578 5749 6170950 5981 6811 6410 8423
NO 4500 3963 4076 43561000 4230 4781 4515 6201
NO 2562 2886 2961 31491050 3065 3433 3256 4687
YES 105249 5030 13356 1 1000 5851 16146 8686 11722 41599
YES 39976 3532 8297 9693 1050 9837 5805 7493 21172
YES 15883 2539 5254 6035 1100 6102 3953 4877 11382
Table 2 – Fatigue life predictions by the strain life and strain energy density life approach.
Strain Energy Density Life Approach
Life Predicted [Cycles]
SPCSA
Stress[MPa]
Experimental[Cycles]
StrainLife
Approach[cycles] efx [mm]
efx(fromLCFtest)
efx (fromWasher
specimenNoSP)
efx..0(fromLCFtest)
efx..0 (from Washer
specimenNoSP)
NO 59193 26473 0.425 1 800 7396 52833 8500 53678
NO 29393 12466 0.478 6992 25267 5133 26770 850
NO 15191 6674 0.535 4484 12191 3621 12728 900
NO 8137 3962 0.674 3 950 624 7510 2783 6011
NO 4500 2613 0.758 1000 2498 2454 2233 2763
NO 2562 1865 0.852 1050 2122 1326 1867 1309
YES 105249 3633 0.244 1689 483 7089 43584 1000
YES 39976 2359 0.244 1496 262 3850 14790 1050
YES 15883 1666 0.244 1405 188 2678 5299 1100
Fatigue life predictions for the total strain energy density
taken at a distance efx are identified in Table 2 by “Life at
efx ” (from LCF test) where the curve used to relate energy
with number of cycles was obtained from LCF tests whose
parameters are in section 3. If the curve energy-life is
obtained from the experimental results for the washer
specimen without shot peening, the life predicted is in the
next column identified by “from Washer specimen NoSP”.
The last two columns refer to a different approach in which
the equivalent strain energy was averaged from surface up to
the effective distance, such as the SFI model. This method
has been used by Lanning, Nicholas et al. [30].
Observing the results obtained when effective strain energy
is taken at a distance efx , life predictions give much lower
life than expected. For the shot peening condition results are
much worse. However if the equivalent total strain energy
density is taken not at efx but averaged from efx..0 , the
predicted results are quite close to the experimental ones.
5. DISCUSSION
In section 5 several numerical fatigue life predictions were
made, by applying total fatigue life methods. The objective
was to numerically obtain fatigue life for the washer
specimens experimentally tested in the conditions with and
without residual stress due to shot peening. From the
literature, no previous work has made predictions of fatigue
life for components with high stress concentrations and shot
peening under LCF conditions. Some of the methods used
for fatigue life evaluation are not appropriate for these
conditions. Even so, the most common methods were used
to check if any of these can be used to predict life for all the
conditions experimentally tested.
The results of fatigue life predictions using the stress life
approach are in Table 1. Comparing these results with
experimental ones, Figure 8, it is possible to see that the
differences are significant, but predictive values are always
conservative. Volumetric approaches that consider large
R. A. Cláudio et al. Fatigue Life Prediction of Shot Peening
104 Ciência e Tecnologia dos Materiais, Vol. 20, n.º 1/2, 2008
R. A. Cláudio et al. Fatigue Life Prediction of Shot Peening
104 Ciência e Tecnologia dos Materiais, Vol. 20, n.º 1/2, 2008
distances from the surface (such as the line method or the
SFI method) give fatigue lives that are closer to the
experimental results. The SFI method is very difficult to
apply because the criterion used to determine the critical
distance does not work for LCF whether or not residual
stress is included. Even when trying to introduce other
criterion in order to define the critical distance, there is no
way to fit the experimental observations for all situations
studied. As seen in Table 1 and Figure 8, the El Haddad et al. distance fatigue life predictions are too pessimistic.
According to the initial expectation, stress life methods are
not appropriate for life prediction under LCF conditions,
leading to conservative results.
1000
10000
100000
1000000
1000 10000 100000 1000000
NumerirrciiacclPllrPPerrdeeiddciitccttottiitttt
ns
StSSrtterrseesss
LiLLfiieffiiii
ApAA
ppp
rorracaah[hhC[[yCC
cyylellsee]ss
Experimental life [Cycles]
Hot Spot Stress NoSP Hot Spot Stress SP
Line 2a0 NoSP Line 2a0 SP
Line 0.1mm NoSP Line 0.1mm SP
Line 0.1mm + Phi(x) NoSP Line 0.1mm + Phi(x) SP
Line 0.2mm NoSP Line 0.2mm SP
Line 0.2mm + Phi(x) NoSP Line 0.2mm + Phi(x) SP
SFI NoSP SFI SP
Fig. 8. Experimental results vs numerical predictions of
fatigue life calculated by the stress life approach.
The results predicted by the strain life approach, given in
Table 2 are also plotted in Figure 9 against the experimental
results. Life predicted by this method is always inferior to
the experimental observations. For the shot peened
condition these results give less than 1/10th
of the expected
life. The main reason is because strain and stress are taken at
the surface where the condition is almost the same (both
with and without shot peening). This criterion is frequently
used to determine crack initiation because parameters are
taken from the surface, where initiation normally occurs. If
these results refer to crack initiation, the predicted life may
be in agreement with many observations found in the
literature. In fact many researchers argue that the principal
benefit of shot peening is in the ability to retard or stop
microcrack propagation pointing out that residual stress has
no influence on initiation [31-33]. From the experimental
tests, many specimens did not fail after a large number of
cycles. Burgess [34], analysed some of these specimens
classified as run-outs and concluded that they had a small
crack, in the order of some tens of microns, that arrested,
being once again in agreement with the ability of shot
peening in retarding or stopping microcrack propagation. As
proposed by Cameron and Smith [35], this method can be
used together with a crack propagation law for total fatigue
life determination purposes.
Bentachfine, Pluvinage et al. [36] proposed a method based
on the strain energy density to predict fatigue life for both
HCF and LCF conditions. This method, seems to be
appropriate to determine the fatigue life without shot
peening. In Table 2 and Figure 9 are some fatigue life
predictions results for the cases studied. By comparing these
results with experimental ones, it is possible to find a
reasonable good fit when shot peening is not considered.
However, numerical predictions for shot peening cases do
not give so good results when comparing with the
experimental ones. This is because the effective distance
obtained by the criterion defined by Bentachfine, Pluvinage
et al. [36] falls behind the tensile region of initial residual
stress. Averaging strain energy, between the surface and the
critical distance, (last two columns of Table 2), predictions
for the shot peened condition become close to the
experimental results. Dingquan et al [37], have a similar
opinion, saying that residual stress should be averaged over
a defined depth in order to evaluate the new fatigue limit.
They also maintain that this distance is a material parameter.
However, even when changing the critical distance, the
results do not improve significantly.
1000
10000
100000
1000000
1000 10000 100000 1000000NumerirrciiacclPllrPPerrdeeiddciitccttottiitttt
nsStSSrttarriniiLiLLfiieffiiii
and
StSSrttarriniiEnEE
ergrrygg
LiLLfiieffiiii
ApAA
ppp
rorracaahehhsee
[ssC[[yCC
cyylellsee]ss
Experimental life [Cycles]
Strain NoSP Strain SP
Xef NoSP Xef SP
0..Xef NoSP 0..Xef SP
Xef (ref NoSP) NoSP Xef (ref NoSP) SP
0..Xef (ref NoSP) NoSP 0..Xef (ref NoSP) SP
Fig. 9. Experimental results vs numerical predictions of
fatigue life calculated by the strain life and strain energy life
approaches.
5. CONCLUSIONS
Fatigue life calculated using total fatigue life predictive
methods which are normally used for notched geometries,
gave conservative results for almost all of the situations
herein studied. These were found to be too pessimistic in
predicting the shot peening effect. Results are much better if ff
stress or strain energy density is averaged over a critical
distance, when shot peening is considered.
The strain life method gave the most conservative results. In
this case, fatigue life predictions with and without shot
peening is almost the same, which is not in agreement with
the experimental results. However this conclusion may be in
agreement with many observations from other researchers
which argue that shot peening has the ability to retard or
stop microcrack propagation instead of avoiding crack
initiation. If these affirmations are correct, then this
approach could be used in methods like Cameron and Smith
method [35] which combine crack initiation with crack
propagation predictions.
The strain energy density life prediction approach, according
to [36], provides results quite close to the experimental
observations for all cases studied without shot peening.
However if residual stress is considered, this method does
not provide reliable life predictions. The principal
limitations are due to the difficulty in defining the critical
distance since gradients are extremely high close to the
scratch when shot peening is considered.
Fatigue Life Prediction of Shot Peening R. A. Cláudio et al.
Ciência e Tecnologia dos Materiais, Vol. 20, n.º 1/2, 2008 105
Fatigue Life Prediction of Shot Peening R. A. Cláudio et al.
Ciência e Tecnologia dos Materiais, Vol. 20, n.º 1/2, 2008 105
ACKNOWLEDGEMENTS
The authors would like to thank to RTO/NATO, FCT for funding and ongoing support.
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